SA-SUPPLEMENT SUBMODULES


Durgan Y.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.58, no.1, pp.147-161, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.4134/bkms.b200128
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.147-161
  • Keywords: Proper class of short exact sequences, sa-supplement submodule, sa-supplementing modules, semiartinian modules, MODULES

Abstract

In this paper, we introduced and studied sa-supplement submodules. A submodule U of a module V is called an sa-supplement submodule in V if there exists a submodule T of V such that V = T +U and U boolean AND T is semiartinian. The class of sa-supplement sequences SAS is a proper class which is generated by socle-free modules injectively. We studied modules that have an sa-supplement in every extension, modules whose all submodules are sa-supplement and modules whose all sasupplement submodules are direct summand. We provided new characterizations of right semiartinian rings and right SSI rings.